Characterization of Mixing Length Growth for Flow in Heterogeneous Porous Media

Abstract

ABSTRACT The scale up problem concerns the prediction of field scale fluid flow properties from smaller scale (laboratory) data. It has been observed from field data that the mixing length for two phase flow has anomalous scaling behavior. Recent theoretical and computational developments have confirmed that anomalous scaling behavior results from multi-length scale heterogeneities not observable at laboratory length scales. Two main results are presented here. One is a generalization of the fractal analysis of rock and fluid mixing properties, as a first step in moving from idealized self-similar reservoir properties to realistic geology. The other is a refinement of earlier computational results demonstrating anomalous diffusion for flow through reservoirs with weakly decaying fractal correlations.